A206138 G.f.: A(x) = Sum_{n>=0} x^(n*(n+1)/2) / Product_{k=1..n} (1-x^k)^k.

1, 1, 1, 2, 2, 4, 5, 8, 10, 17, 21, 32, 44, 62, 86, 122, 164, 230, 318, 428, 591, 803, 1088, 1467, 1995, 2665, 3596, 4800, 6430, 8552, 11416, 15093, 20062, 26487, 34988, 46035, 60626, 79490, 104278, 136337, 178189, 232331, 302724, 393493, 511165, 662775, 858380

Offset

0,4

Links

Table of n, a(n) for n=0..46.

Example

 G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 2*x^4 + 4*x^5 + 5*x^6 + 8*x^7 ...
where
A(x) = 1 + x/(1-x) + x^3/((1-x)*(1-x^2)^2) + x^6/((1-x)*(1-x^2)^2*(1-x^3)^3) + x^10/((1-x)*(1-x^2)^2*(1-x^3)^3*(1-x^4)^4) +...

Prog

 (PARI) {a(n)=polcoeff(sum(m=0, n, x^(m*(m+1)/2)/prod(k=1, m, (1-x^k +x*O(x^n))^k)), n)}
for(n=0, 60, print1(a(n), ", "))

Crossrefs

Cf. A206100.

Sequence in context: A126796 A325831 A240451 * A241545 A157162 A109434

Adjacent sequences: A206135 A206136 A206137 * A206139 A206140 A206141

Keyword

nonn

Author

Paul D. Hanna, Feb 04 2012

Status

approved